%I #9 Mar 19 2021 07:08:01

%S 0,0,1,0,-2,3,0,0,-9,7,0,8,0,-28,15,0,0,60,0,-75,31,0,-96,0,280,0,

%T -186,63,0,0,-1008,0,1050,0,-441,127,0,2176,0,-6272,0,3472,0,-1016,

%U 255,0,0,29376,0,-30240,0,10584,0,-2295,511,0,-79360,0,228480,0,-124992,0,30480,0,-5110,1023

%N T(n, k) = [x^k] 2^n*(Euler(n, x) - Euler(n, x/2)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.

%e Table starts:

%e [0] 0

%e [1] 0, 1

%e [2] 0, -2, 3

%e [3] 0, 0, -9, 7

%e [4] 0, 8, 0, -28, 15

%e [5] 0, 0, 60, 0, -75, 31

%e [6] 0, -96, 0, 280, 0, -186, 63

%e [7] 0, 0, -1008, 0, 1050, 0, -441, 127

%e [8] 0, 2176, 0, -6272, 0, 3472, 0, -1016, 255

%e [9] 0, 0, 29376, 0, -30240, 0, 10584, 0, -2295, 511

%p CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):

%p E := (n, x) -> 2^n*(euler(n, x) - euler(n, x/2));

%p 0,seq(CoeffList(E(n, x)), n = 0..10);

%Y Cf. A060096/A060097, A163747 (row sums).

%K sign,tabl

%O 0,5

%A _Peter Luschny_, Mar 19 2021